I'd say, it depends on the person, but for the most part, if you've tickled her fancy, she'll make the effort to maintain the communication and go out with you. This has been my experience. Also too, if you don't maintain the communication, she'll take it as not being interested. I did this with a girl once, we went out, but I never really "initiated" anything because I was too anxious, and it never went anywhere. The other time I did pretty much the same thing, we went out, but after that I never called her. But this time, I took it as she really wasn't too interested, so I never bothered to maintain communication like I should of, and she thought I wasn't interested. So, both times, I did not maintain communication, either because I was to anxious, or did not properly read her to tell if she was interested.
What usually happens with me, is if they don't initiate, like in those two situations, it ends up like it did in those two situations. In these situations, it usually brings me down because I'm the one who failed, and I could have kept up the communication and made the dates successful, but because I couldn't read what was going on or was too anxious, the dates ended up in failure. The previous two girlfriends I had both were outgoing, and initiated quite a bit, so things went successful until we broke up.